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## Definition: Prime Field

A prime field $(P, + ,\cdot)$ is a field does not contain any proper subfields. Formally, if $(F, + ,\cdot)$ is a field, then $P$ is the algebraic structure defined by $$P:=\bigcap_{S\subset F,\;S\text{ subfield of }F}S.$$

| | | | | created: 2019-08-10 07:12:33 | modified: 2019-08-10 07:32:54 | by: bookofproofs | references: [677]

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